# QUANTITATIVE APTITUDE -Mensuration Important Formulas

Rectangle :
Area = lb
Perimeter
= 2(l+b)
Square :
Area = a×a
Perimeter
= 4a
Parallelogram
Area = l ×
h
Perimeter
= 2(l+b)
Triangle :
Area
=b×h/2 or √s(s-a)(s-b)(s-c)…………….where s=a+b+c/2
Right angle Triangle :
Area
=1/2(bh)
Perimeter
= b+h+d
Isosceles right angle triangle :
Area = ½.
a2
Perimeter
= 2a+d……………………….where d=a√2
Equilateral Triangle :
Area = √3.
a2/4 or  ½(ah)….where h = √3/2
Perimeter
= 3a
Trapezium :
Area =
1/2h(a+b)
Perimeter
= Sum of all sides
Rhombus :
Area = d1
× d2/2
Perimeter
= 4l
Area =1/2
× Diagonal × (Sum of offsets)
Kite :
Area
= d1×d2/2
Perimeter
= 2 × Sum on non-adjacent sides
Circle :
Area =
πr^2 or πd^2/4
Circumference
= 2πr  or πd
Area of
sector of a circle = (θπr^2 )/360
Frustum :
Curved
surface area = πh(r1+r2)
Surface
area = π( r12+ h(r1+r2) + r22)
Cube :
Volume: V
= l3
Lateral
surface area = 4a2
Surface
Area: S = 6s2
Diagonal
(d) = √3l
Cuboid :
Volume of
cuboid: lbh
Total
surface area = 2 (lb + bh + hl) or 6l2
Length of
diagonal =√(l^2+b^2+h^2)
Right Circular Cylinder :
Volume of
Cylinder = π r2 h
Lateral
Surface Area (LSA or CSA) = 2π r h
Total
Surface Area = TSA = 2 π r (r + h)
Volume of
hollow cylinder = π r h(R2 – r2)
Right Circular cone :
Volume =
1/3 π r2h
Curved
surface area: CSA=  π r l
Total
surface area = TSA = πr(r + l )
Sphere
Volume: V
= 4/3 πr3
Surface
Area: S = 4πr2
Hemisphere :
Volume =
2/3 π r3
Curved
surface area(CSA) = 2 π r2
Total
surface area = TSA = 3 π r2
Prism :
Volume =
Base area x h
Lateral
Surface area = perimeter of the base x h
Pyramid:
Volume of
a right pyramid = (1/3) × area of the base × height.
Area of
the lateral faces of a right pyramid = (1/2) × perimeter of the base x slant
height.
Area of
whole surface of a right pyramid = area of the lateral faces + area of the
base.
Tetrahedron :
Area of
its slant sides = 3a2√3/4
Area of
its whole surface = √3a2
Volume of
the tetrahedron = (√2/12) a 3
Regular Hexagon :
Area
=  3√3 a2 / 2
Perimeter
= 6a
Some other Formula :
Area of
Pathway running across the middle of  a rectangle = w(l+b-w)
Perimeter
of Pathway around a rectangle field = 2(l+b+4w)
Area of
Pathway around a rectangle field =2w(l+b+2w)
Perimeter
of Pathway inside a rectangle field =2(l+b-4w)
Area of
Pathway inside a rectangle field =2w(l+b-2w)
Area of
four walls = 2h(l+b)